81777 ÷ 5 = 16355 R2
Alright, let's work through the division of 81777 by 5 step by step.

Step 1:
5 goes into 8 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 8 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 5

Step 2:
5 goes into 31 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 30 from 31 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 5

Step 3:
5 goes into 17 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 163
Subtract 15 from 17 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 5

Step 4:
5 goes into 27 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 1635
Subtract 25 from 27 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 5

Step 5:
5 goes into 27 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 16355
Subtract 25 from 27 to get 2.

The final result is 16355 with a remainder of 2.